Question

$3(x+1)=-\frac{1}{2}-5x$
Which of the following best describes the solution set to the equation shown above ?

• A. The equation has no solution.
• B. The equation has exactly one solution, $x=-\frac{7}{16}$
• C. The equation has exactly one solution, $x=-\frac{7}{4}$
• D. The equation has infinitely many solutions

Answer 1

The correct option is B The equation has exactly one solution, $x=-\frac{7}{16}$

$3(x+1)=-\frac{1}{2}-5x$
$3x+3=-\frac{1}{2}-5x$
Add 5x on both sides and substract 3 from both sides
$3x+3+5x-3=-\frac{1}{2}-5x+5x-3$
$8x+3=-\frac{1}{2}-3$
$8x=-\frac{7}{2}$
$x=-\frac{7}{16}$
The equation has exactly one solution, $x=-\frac{7}{16}$

Hence, option B is correct.